METHOD OF SOLVING LINEAR PROGRAMMING PROBLEMS

Linear programming is one of the most effective techniques used in decision-making and optimization problems, especially in business and industrial applications. This project focuses on the use of a linear programming to determine the most efficient way of maximizing profit and minimizing cost. Mouka Foam Company, Benin City, was used as a case study to demonstrate how mathematical models can support better production and resource allocation decisions The simplex method was applied to the formulated linear programming problem derived from the assumed but realistic data of Mouka Foam Company. The process involved defining the objective function, identifying the constraints, introducing slack variables, and systematically applying the simplex algorithm to reach an optimal solution. The entire computation was manually solved and verified to ensure the accuracy of results The result of the analysis shows that the simplex method provided an optimal solution that maximizes profit while minimizing production cost under the given constraints. The findings prove that linear programming is a reliable and efficient mathematical tool for managerial decision-making, especially in production planning and cost optimization.